On the Stiffness Matrix of an Element of Space Framework

Abstract

The geometrical stiffness matrix plays a significant role in the problems of large deflection or instability problems of space framework. In conventional analysis, only the effect of initial axitial force has been considered in the geometrical stiffness matrix. This paper shows that, in addition, initial bending moment and torsional moment terms have to be included in stiffness matrix. Its theoretical derivation are developed using the matrix displacement method based on the principle of virtual work. And some numerical examples of initial instability problems are presented to demonstrate the validity of the theory deduced.